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A finite characterization of weak lumpable Markov processes. Part I: The discrete time case

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  • Rubino, Gerardo
  • Sericola, Bruno

Abstract

We consider an irreducible and homogeneous Markov chain (discrete time) with finite state space. Given a partition of the state space, it is of interest to know if the aggregated process constructed from the first one with respect to the partition is also Markov homogeneous. We give a characterization of this situation by means of a finite algorithm. This algorithm computes the set of all initial probability distributions of the starting homogeneous Markov chain leading to an aggregated homogeneous Markov chain.

Suggested Citation

  • Rubino, Gerardo & Sericola, Bruno, 1991. "A finite characterization of weak lumpable Markov processes. Part I: The discrete time case," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 195-204, August.
    • Handle: RePEc:eee:spapps:v:38:y:1991:i:2:p:195-204
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    Cited by:

    1. Spreij, Peter, 2001. "On the Markov property of a finite hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 279-288, April.
    2. Stadje, Wolfgang, 2005. "The evolution of aggregated Markov chains," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 303-311, October.
    3. Levi John Wolf & Sergio Rey, 2016. "On the lumpability of regional income convergence," Letters in Spatial and Resource Sciences, Springer, vol. 9(3), pages 265-275, October.
    4. Ledoux, James, 1995. "On weak lumpability of denumerable Markov chains," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 329-339, December.

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